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arXiv · 2307.03282

Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics

Nicoló Drago·Sonia Mazzucchi·Valter Moretti
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Abstract

In this work we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The main tools we use are the Cartan development map, the notion of oscillatory integral, and the Chernoff approximation theorem. We prove that, for a class of functions of a dense subspace of the relevant Hilbert space, the Feynman map produces the solution of the Schr\"odinger equation, where the Laplace-Beltrami operator coincides with the second order Casimir operator of the group.

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Nicoló Drago, Sonia Mazzucchi, Valter Moretti. 2023-07-06. Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics. https://arxiv.org/abs/2307.03282

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